Question

Find the sum of all mutiples of 7 lying between 500-900 in arithmetic progression 0

Answer 1

I made the assumption of 500 - 900 INCLUSIVE

My PYTHON program:

sum = 0

for x in range (500, 901):

if x % 7 != 0:

sum += x

print()

print ('Sum = {:,}'.format(sum))

Sum = 240,800

Answer 2

900/7  = 128.57

l = 7 x 128 = 896

500/7 = 71.43

a = 72 x 7 = 504

896 = 504 + (n - 1)7

896 - 504 = 7n - 7

392 + 7 = 7n

n  = 399 /7 = 57

Sum = n/2 (a + l )                 or you can use n/2 [2a + (n-1)d]

57/2 ( 504 + 896)                          57/2 [2x 504 + (57 -1) 7}

57/2 x 1400                                    57/2  x (1008 + 392)

57 x 700 = 39900                          57/2  x 1400  = 57 x 700 = 39900

Answer is 39900